Question

Old question: Show that a translation \(T_{PQ}\) is equivalent to the composition of 2 reflections in parallel lines l1 and l2 where l1 , l2 are perpendicular to PQ. If d is distance between l1 and l2, show PQ = 2d Please, help

Answer 1

Wow!!! who is there??? long time no see, friend. How are you?

Answer 2

@pitamar

Answer 3

All good thanks =) how are you?

Answer 4

Good!! thank you.

Answer 5

This is my attempt: Let PQ be an arbitrary segment, let l1 perpendicular to PQ at A, let \(R_{l1}\) be reflection on l1 and hence, \(R_{l1}(P) = P' ~~R_{l1}(Q)=Q'\). \(R_{l1}\) is isometry, hence PQ = P'Q'